Solve for x 2/( square root of 3)*cos(3x)=1

Problem

2/√(,3)*cos(3*x)=1

Solution

1. Isolate the cosine term by multiplying both sides of the equation by √(,3)/2

cos(3*x)=√(,3)/2

2. Identify the reference angle for which the cosine value is √(,3)/2 which is π/6 (or 30^∘.

cos(π/6)=√(,3)/2

3. Determine the general solutions for the argument 3*x using the unit circle, noting that cosine is positive in Quadrants I and IV.

3*x=±π/6+2*k*π

4. Solve for x by dividing the entire expression by 3

x=±π/18+(2*k*π)/3

Final Answer

2/√(,3)*cos(3*x)=1⇒x=±π/18+(2*k*π)/3

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